The Choice of Basis Functions in event-related fMRI
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The Choice of Basis Functions in event-related fMRI
Choices of basis functions include a Fourier set [1], lagged gamma functions [2], or a canonical response function and its partial derivatives [3]. Another choice is ...
The Choice of Basis Functions in event-related fMRI Richard Henson, Michael Rugg & Karl Friston Wellcome Department of Cognitive Neurology and Institute of Cognitive Neuroscience, University College London, London, U.K. To accommodate variability in its shape, the BOLD impulse response can be modelled by a set of basis functions within the General Linear Model (GLM). Choices of basis functions include a Fourier set [1], lagged gamma functions [2], or a canonical response function and its partial derivatives [3]. Another choice is a Finite Impulse Response (FIR) set, which captures any shape of response up to a given frequency limit. We discuss its practical advantages, and contrast it with the partial derivatives of a canonical function. Advantages The FIR set consists of a number of successive poststimulus timebins (“mini-boxcars”). The implementation of the FIR set in a GLM effectively averages the BOLD response at each poststimulus time (without requiring counterbalancing of stimuli [2]). These averages, corresponding to the parameter estimate for each timebin, can be entered into univariate analyses-of-variance with time as a factor (with appropriate corrections for nonsphericity), or multivariate analyses [4]. Inspection of timecourses may be necessary to confirm that effects are haemodynamic (rather than, say, movement artifact). Alternatively, assumptions about the shape of the BOLD response can be realised by appropriately weighted contrasts of the parameter estimates (without needing to refit a model). Comparison Twelve subjects made fame judgments on faces using a right finger press. Faces were presented for 500ms against a2 baseline chequerboard, with an exponential distribution of SOAs (minimal=4.5s). Echoplanar images (3x3mm pixels, TE=40ms, TR=2s) were acquired at 2T with blood oxygenation level dependent (BOLD) contrast. Images were realigned spatially and temporally, normalised, smoothed by 8mm and highpass filtered to 1/120Hz. Serial autocorrelations were modelled with an AR(1) model. Famous and nonfamous faces were modelled with both a “canonical” set of three functions - the canonical response, its temporal derivative and its dispersion derivative [3] - and an FIR set of twelve 2s bins from 0-24s poststimulus (Fig. 1). Fixed-effect F-tests on the main effect of faces, collapsing across subjects, were thresholded at p
